{"id":"https://openalex.org/W2094794197","doi":"https://doi.org/10.1109/tit.2015.2417051","title":"Stable Embedding of Grassmann Manifold via Gaussian Random Matrices","display_name":"Stable Embedding of Grassmann Manifold via Gaussian Random Matrices","publication_year":2015,"publication_date":"2015-03-25","ids":{"openalex":"https://openalex.org/W2094794197","doi":"https://doi.org/10.1109/tit.2015.2417051","mag":"2094794197"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2015.2417051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2417051","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015917634","display_name":"Hailong Shi","orcid":"https://orcid.org/0000-0001-7875-3668"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hailong Shi","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China","Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100396885","display_name":"Hao Zhang","orcid":"https://orcid.org/0000-0002-2928-2692"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Zhang","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China","Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100438655","display_name":"Gang Li","orcid":"https://orcid.org/0000-0001-9755-2781"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Li","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China","Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003384431","display_name":"Xiqin Wang","orcid":"https://orcid.org/0000-0002-6980-0466"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiqin Wang","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China","Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, CHINA#TAB#","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015917634"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":2.3453,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87152842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"5","first_page":"2924","last_page":"2941"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.7639874219894409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7137112617492676},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7127265930175781},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5912517309188843},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4885886609554291},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4306091070175171},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.429715633392334},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4236491918563843},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.421403706073761},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.41075536608695984},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.37197259068489075},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31688475608825684},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2804333567619324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2658367455005646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2287616729736328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1989043653011322},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17029011249542236}],"concepts":[{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.7639874219894409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7137112617492676},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7127265930175781},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5912517309188843},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4885886609554291},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4306091070175171},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.429715633392334},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4236491918563843},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.421403706073761},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.41075536608695984},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.37197259068489075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31688475608825684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2804333567619324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2658367455005646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2287616729736328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1989043653011322},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17029011249542236},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2015.2417051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2015.2417051","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.749.8282","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.749.8282","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1312.3263.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2496957729","display_name":null,"funder_award_id":"61422110","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3484506148","display_name":null,"funder_award_id":"61201356","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4959846173","display_name":null,"funder_award_id":"41271011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6330363091","display_name":null,"funder_award_id":"NCET-11-0270","funder_id":"https://openalex.org/F4320334924","funder_display_name":"Program for New Century Excellent Talents in University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W340244495","https://openalex.org/W1591116419","https://openalex.org/W1970453577","https://openalex.org/W1986736933","https://openalex.org/W1997516668","https://openalex.org/W1999174140","https://openalex.org/W2015418199","https://openalex.org/W2020120128","https://openalex.org/W2030449718","https://openalex.org/W2037322760","https://openalex.org/W2037461019","https://openalex.org/W2044762091","https://openalex.org/W2049449022","https://openalex.org/W2074863717","https://openalex.org/W2080323335","https://openalex.org/W2093427575","https://openalex.org/W2102701524","https://openalex.org/W2103955025","https://openalex.org/W2104608642","https://openalex.org/W2105877514","https://openalex.org/W2108036604","https://openalex.org/W2109379066","https://openalex.org/W2115139597","https://openalex.org/W2120695425","https://openalex.org/W2120732454","https://openalex.org/W2120961178","https://openalex.org/W2125680629","https://openalex.org/W2126017757","https://openalex.org/W2129131372","https://openalex.org/W2131172946","https://openalex.org/W2133214726","https://openalex.org/W2143168132","https://openalex.org/W2143769908","https://openalex.org/W2145096794","https://openalex.org/W2147276092","https://openalex.org/W2147631863","https://openalex.org/W2159268085","https://openalex.org/W2162409952","https://openalex.org/W2164094257","https://openalex.org/W2164799551","https://openalex.org/W2167853904","https://openalex.org/W2169448252","https://openalex.org/W2196956961","https://openalex.org/W2296616510","https://openalex.org/W2323918938","https://openalex.org/W2610857016","https://openalex.org/W2963607629","https://openalex.org/W3101990100","https://openalex.org/W3105910849","https://openalex.org/W3125735862","https://openalex.org/W4229706427","https://openalex.org/W4235713725","https://openalex.org/W4240930380","https://openalex.org/W4250955649","https://openalex.org/W4300263211","https://openalex.org/W4300541453","https://openalex.org/W6655786889","https://openalex.org/W6675827639","https://openalex.org/W6679168169","https://openalex.org/W6684851707"],"related_works":["https://openalex.org/W2598603320","https://openalex.org/W2049271832","https://openalex.org/W2001022371","https://openalex.org/W2067278681","https://openalex.org/W4289294429","https://openalex.org/W1551994473","https://openalex.org/W2148623659","https://openalex.org/W3101763414","https://openalex.org/W2899750798","https://openalex.org/W3215788575"],"abstract_inverted_index":{"Compressive":[0],"sensing":[1],"(CS)":[2],"provides":[3],"a":[4,43,53,90,110,118,191,213,228,267],"new":[5],"perspective":[6],"for":[7,28,130,183,195,315],"data":[8],"reduction":[9],"without":[10],"compromising":[11],"performance":[12],"when":[13],"the":[14,31,39,62,75,142,153,158,161,171,177,184,198,207,232,240,256,262,281,286,295,302],"signal":[15,148],"of":[16,30,46,55,64,70,78,94,163,165,173,186,209,231,243,245,250,271,288],"interest":[17],"is":[18,36,109,117,123,227,278,298],"sparse":[19,50],"or":[20,51],"has":[21],"intrinsically":[22],"low-dimensional":[23],"structure.":[24],"The":[25,106],"theoretical":[26],"foundation":[27],"most":[29],"existing":[32,68],"studies":[33],"on":[34,38,98,152,197,266,294],"CS":[35,71],"based":[37,97],"stable":[40,76,92,234,263],"embedding":[41,77,93,193,225,235,258,264],"(i.e.,":[42],"distance-preserving":[44],"property)":[45],"vectors":[47,149,246],"that":[48,280],"are":[49,219,312],"in":[52,113,216,247,301],"union":[54],"subspaces":[56,80],"via":[57,81,101,201,305],"random":[58,103,203,307],"measurement":[59,83,104,204,308],"matrices.":[60,105,309],"To":[61],"best":[63],"our":[65],"knowledge,":[66],"few":[67],"literatures":[69],"have":[72],"clearly":[73],"discussed":[74],"linear":[79,119,135,143],"compressive":[82],"systems.":[84],"In":[85,137,252],"this":[86,138],"paper,":[87,139],"we":[88,140,254],"explore":[89,261],"volume-based":[91],"multidimensional":[95,131,147,229],"signals":[96,132],"Grassmann":[99,107,154,187,199,217,272,296],"manifold,":[100,155,297],"Gaussian":[102,202,306],"manifold":[108,200,218,273],"topological":[111],"space,":[112],"which":[114,237],"each":[115],"point":[116],"vector":[120],"subspace,":[121],"and":[122,156,160,180],"widely":[124],"regarded":[125],"as":[126,150,170,176],"an":[127],"ideal":[128],"model":[129],"generated":[133],"from":[134,212,275],"subspaces.":[136,251],"formulate":[141],"subspace":[144],"spanned":[145],"by":[146],"points":[151,196,293],"use":[157,255],"volume":[159],"product":[162,172,287],"sines":[164,290],"principal":[166,174,289],"angles":[167],"(also":[168],"known":[169],"sines)":[175],"generalized":[178,268,282],"norm":[179],"distance":[181,269,283],"measure":[182,270],"space":[185],"manifold.":[188],"We":[189],"prove":[190],"volume-preserving":[192,224,257],"property":[194,226,259],"matrices,":[205],"i.e.,":[206,285],"volumes":[208],"all":[210],"parallelotopes":[211],"finite":[214],"set":[215],"preserved":[220,300],"upon":[221],"compression.":[222],"This":[223],"generalization":[230],"conventional":[233],"properties,":[236],"only":[238],"concern":[239],"approximate":[241],"preservation":[242],"lengths":[244],"certain":[248],"unions":[249],"addition,":[253],"to":[260],"effect":[265],"induced":[274],"volume.":[276],"It":[277],"proved":[279],"measure,":[284],"between":[291],"different":[292],"well":[299],"compressed":[303],"domain":[304],"Numerical":[310],"simulations":[311],"also":[313],"provided":[314],"validation.":[316]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}